# IA-automorphism-invariant subgroup

From Groupprops

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

A subgroup of a group is termed an **IA-automorphism-invariant subgroup** if it is invariant under all IA-automorphisms of the whole group.

## Formalisms

### Function restriction expression

This subgroup property is a function restriction-expressible subgroup property: it can be expressed by means of the function restriction formalism, viz there is a function restriction expression for it.

Find other function restriction-expressible subgroup properties | View the function restriction formalism chart for a graphic placement of this property

The property of being an IA-automorphism-invariant subgroup is the invariance property with respect to IA-automorphisms, and has the function restriction expression:

IA-automorphism Function

In particular, it is an endo-invariance property with function restriction expression:

IA-automorphism Endomorphism

In fact, since inverses of IA-automorphisms are IA-automorphisms, it is an auto-invariance property with function restriction expression:

IA-automorphism Automorphism